Analysis of Multiwindow Gabor-Type Schemes by Frame Methods☆
Analysis of Multiwindow Gabor-Type Schemes by Frame Methods☆
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DOI：
10.1006/acha.1997.0209
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发表时间：
1997-04
影响因子：
2.5
通讯作者：
M. Zibulski;Y. Zeevi
中科院分区：
文献类型：
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作者：
M. Zibulski;Y. Zeevi
摘要将Gabor格式推广到包含多种窗函数以及指数函数以外的核函数。用一种基于框架概念的方法来表征表示函数序列的性质。利用分段Zak变换（PZT），通过将帧算子表示为PZT域中的有限阶矩阵值函数来检查与多窗口gabor型帧相关的帧算子是否具有合理的过采样率。结合矩阵值函数的性质，研究了表示函数序列的完备性和框架性。考虑了框架边界和双框架的计算，以及紧框架问题。结果表明，用其他核代替广泛使用的指数核，基本上不会改变表示函数序列的性质。还考虑了一些例子和每个窗口不同采样率的问题。所谓的bali - low定理被推广到考虑多窗口方案，这使得在某种程度上有可能克服原定理在单窗口情况下所施加的约束。
Abstract The Gabor scheme is generalized to incorporate several window functions as well as kernels other than the exponential. The properties of the sequence of representation functions are characterized by an approach based on the concept of frames. Utilizing the piecewise Zak transform (PZT), the frame operator associated with the multiwindow Gabor-type frame is examined for a rational oversampling rate by representing the frame operator as a finite-order matrix-valued function in the PZT domain. Completeness and frame properties of the sequence of representation functions are examined in relation to the properties of the matrix-valued function. Calculations of the frame bounds and the dual frame, as well as the issue of tight frames, are considered. It is shown that the properties of the sequence of representation functions are essentially not changed by replacing the widely used exponential kernel with other kernels. Some examples and the issue of a different sampling rate for each window are also considered. The so-called Balian–Low theorem is generalized to consideration of a scheme of multiwindows which makes it possible to overcome in a way the constraint imposed by the original theorem in the case of a single window.